{
  "id": "2401.09215",
  "version": "v1",
  "published": "2024-01-17T13:54:38.000Z",
  "updated": "2024-01-17T13:54:38.000Z",
  "title": "Topological properties of caustics in five-dimensional spaces",
  "authors": [
    "Vyacheslav D. Sedykh"
  ],
  "comment": "11 pages. arXiv admin note: text overlap with arXiv:2310.15748",
  "categories": [
    "math.AG",
    "math.SG"
  ],
  "abstract": "We give a list of universal linear relations between the Euler characteristics of manifolds consisting of multisingularities of a generic Lagrangian map into a five-dimensional space. From these relations it follows, in particular, that the numbers $D_5A_2, A_4A_3, A_4A_2^2$ of isolated self-intersection points of the corresponding types on any generic compact four-dimensional caustic are even. The numbers $D_4^+A_3+D_4^-A_3+E_6$, $D_4^+A_2^2+D_4^-A_2^2+\\frac12A_4A_3$ are even as well.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-01-17T13:54:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14P25",
      "14Q30",
      "53D12",
      "57R45",
      "58K15",
      "58K35"
    ],
    "keywords": [
      "five-dimensional space",
      "topological properties",
      "generic compact four-dimensional caustic",
      "generic lagrangian map",
      "universal linear relations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}